# Analyzing Graphs of Quadratic Functions

• Nov 4th 2009, 01:15 PM
Quincy Goss
Analyzing Graphs of Quadratic Functions
I'm having extreme trouble doing these problems. Could someone please help me out. Step by step.

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening.

1. Y= (x-2)^2

2. Y= -x^2 + 4

3. Y= x^2 - 6

4. Y= -3(x + 5)^2

5. Y= -5x^2 + 9

6. Y= (x-2)^2 - 18

7. Y= x^2 - 2x - 5

8. Y= x^2 + 6x + 2

9. Y= -3x^2 + 24x
• Nov 4th 2009, 01:50 PM
Jameson
Quote:

Originally Posted by Quincy Goss
I'm having extreme trouble doing these problems. Could someone please help me out. Step by step.

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening.

1. Y= (x-2)^2

2. Y= -x^2 + 4

3. Y= x^2 - 6

4. Y= -3(x + 5)^2

5. Y= -5x^2 + 9

6. Y= (x-2)^2 - 18

7. Y= x^2 - 2x - 5

8. Y= x^2 + 6x + 2

9. Y= -3x^2 + 24x

This is way too many questions for one thread. The best way to learn here is to ask one question and completely get all the concepts behind it. Then you can do the rest of them on your own.

When x is squared, the vertex form is: \$\displaystyle (x-h)^2=4P(y-k)\$. (h,k) is the center. The axis of symmetry is formed by solving the previous equation for y. The opening is upwards if both sides have the same sign. If one if positive and the other negative it opens downwards.

The above info should be review if you are assigned this as homework. Can you do one of the problems now?